First remove the brackets and merge the similar items X - (1-x) + (1-2x)

First remove the brackets and merge the similar items X - (1-x) + (1-2x)

x-（1-x）+（1-2x）
=x-1+x+1-2x
=0

4 (x-1) - 2 (x ^ 2 + 1) - 1 / 2 (4 ^ 2-2x) remove brackets and merge similar items

4 (x-1) - 2 (x ^ 2 + 1) - 1 / 2 (4x ^ 2-2x)
=4X-4-2X^2-2-2X^2+X
=-4X^2+5X-6

Remove the brackets and merge the similar items: (1) x + (2x-1) - (x / 3 + 3) (2) - (B-4) + 4 (- B-3)

（1）x+（2x-1）-（x/3+3）
=x+2x-1-x/3-3
=3x-x/3-4
=8x/3-4
（2）-（b-4)+4(-b-3)
=-b+4-4b-12
=-5b-8

Remove the brackets first, and then merge the similar items: 3 (X-2) + 2 (1-2x)

We get 3x-6 + 2-4x
=(3-4)x-6+2
=-x-4

When hydraulic energy is converted into mechanical energy by motor, how much is the energy loss in general?

Under different pressure and different specifications of the motor, the loss is different. The rotating speed of the hydraulic motor is generally not high, which is related to the design structure. Excessive improvement, low efficiency, serious heating, long-term operation lead to oil deterioration in advance, and even carbon deposition, Hydraulic motor is also called oil motor, five-star motor and five-star oil motor, High speed motor gear motor has the advantages of small volume, light weight, simple structure, good processability, insensitivity to oil pollution, low impact resistance and inertia, etc
Vane motor
Compared with other types of motors, vane motor has the advantages of compact structure, small outline size, low noise and long service life. Its inertia is smaller than that of plunger motor, but its anti pollution ability is worse than that of gear motor, and its speed can not be too high. Generally, it works below 200 R / min. because of large leakage, vane motor is unstable when load changes or low speed
Motor type
Radial piston motor axial piston motor swash shaft piston motor swash plate piston motor low speed hydraulic motor radial piston motor connecting rod hydraulic motor is simple in structure, reliable in operation, various in varieties and specifications, and low in price, No connecting rod hydraulic motor swing cylinder hydraulic motor roller hydraulic motor axial piston motor double swash plate piston motor axial ball plug motor vane motor
orbit motor
In the late 1850s, the original low-speed high torque hydraulic motor was developed from a stator and rotor part of the oil pump, which is composed of an inner ring gear and a matching gear or rotor. The inner ring gear can be connected with the shell, The oil from the oil port drives the rotor around a central point. The slowly rotating rotor is driven by a spline shaft and output to become a cycloid hydraulic motor. After the first cycloid motor came out, after decades of evolution, another concept of motor began to form. The motor is equipped with rollers in the built-in ring gear. The motor with rollers can provide higher starting and running torque, The roller reduces the friction and improves the efficiency. The output shaft can produce stable output even at a very low speed. By changing the direction of input and output flow, the motor can change direction quickly and produce torque of equal value in two directions. Each series of motors has a variety of displacement to meet the requirements of various speeds and torques
Characteristics and classification of hydraulic motors
characteristic
From the point of view of energy conversion, the hydraulic pump and the hydraulic motor are reversible hydraulic components. If the working fluid is input to any kind of hydraulic pump, it will become the working condition of the hydraulic motor. On the contrary, when the main shaft of the hydraulic motor is driven to rotate by the external torque, Because they have the same basic structural elements - closed and periodic volume and corresponding oil distribution mechanism. However, due to the different working conditions of hydraulic motor and hydraulic pump, their performance requirements are also different, so there are still many differences between the same type of hydraulic motor and hydraulic pump, Therefore, the internal structure of the hydraulic motor is required to be symmetrical; the speed range of the hydraulic motor needs to be large enough, especially for its minimum stable speed. Therefore, it usually adopts rolling bearing or hydrostatic sliding bearing; secondly, because the hydraulic motor works under the condition of input pressure oil, it does not need to have self-priming capacity, but it needs certain initial sealing performance, Because of these differences, hydraulic motor and hydraulic pump are similar in structure, but they can't work reversibly
classification
Hydraulic motors can be divided into gear type, vane type, plunger type and other types according to their structural types. According to the rated speed of hydraulic motors, they can be divided into two categories: high speed and low speed, The basic types of high-speed hydraulic motors are gear type, screw type and blade type They are mainly characterized by high speed, small moment of inertia, easy starting and braking, and high sensitivity of adjustment (speed regulation and reversing). Usually, the output torque of high-speed hydraulic motor is small, so it is also called high-speed small torque hydraulic motor. The basic type of low-speed hydraulic motor is radial piston type, In addition, there are low-speed structures in axial piston type, vane type and gear type. The main characteristics of low-speed hydraulic motor are large displacement, large volume and low speed (sometimes up to a few or even zero revolutions per minute), so it can be directly connected with the working mechanism. There is no need for deceleration device, which greatly simplifies the transmission mechanism. Generally, the output torque of low-speed hydraulic motor is large, So it is also called low speed high torque hydraulic motor
Main structure and principle of hydraulic motor
Vane type hydraulic motor
The output torque of the vane type hydraulic motor is related to the displacement of the hydraulic motor and the pressure difference between the inlet and outlet of the hydraulic motor, and its speed is determined by the flow rate of the input hydraulic motor, Therefore, the blade of vane type hydraulic motor should be placed radially. In order to make the blade root always filled with pressure oil, a one-way valve should be set on the passage through which the oil return and pressure chamber pass through the blade root. In order to ensure that the vane type hydraulic motor can start normally after the pressure oil passes through, the top of the blade must be in close contact with the inner surface of the stator to ensure good sealing, Therefore, the pre tightening spring should be set at the root of the blade. The blade type hydraulic motor has small volume, small moment of inertia, sensitive action, and can be applied to the occasions with high commutation frequency; but the leakage is large and unstable at low speed. Therefore, the blade type hydraulic motor is generally used in the occasions with high speed, small torque and sensitive action requirements
Radial piston hydraulic motor
The working principle of radial piston type hydraulic motor is that when the pressure oil enters the bottom of the plunger in the cylinder through the window of the fixed oil distribution shaft 4, the plunger extends outwards and tightly presses against the inner wall of the stator. Because there is an eccentric distance between the stator and the cylinder block, the reaction force of the stator on the plunger is. The force can be divided into two parts. When the oil pressure acting on the bottom of the plunger is p, the reaction force of the stator on the plunger is, When the diameter of the plunger is D and the angle between the force and is x, the force generates a torque on the cylinder block, which makes the cylinder block rotate. The cylinder block then outputs the torque and speed through the transmission shaft connected with the end face, The radial piston hydraulic motor is mostly used in the case of low-speed large inner curve motor torque. 1. The single acting connecting rod radial piston motor is shown in Fig. 4-6, connecting rod motor diagram, axial flow distribution hydraulic motor diagram and five angle radial motor assembly animation, which is the working principle diagram of single acting connecting rod radial piston motor, The motor is composed of shell 1, crankshaft 6, valve shaft 5, connecting rod 3, plunger 2, eccentric wheel 4 and other parts. Advantages: simple structure, reliable operation. Disadvantages: large volume, heavy weight, torque pulsation, The motor is composed of port shaft 1, cylinder block 2, plunger 3, cross beam 4, roller 5, stator 6 and output shaft 7. The displacement of the motor is twice as large as that of the single stroke motor, which is equivalent to 21 plungers, Sometimes this kind of motor is made into multi row plunger, the number of plunger is more, the output torque is further increased, and the torque pulsation rate is further reduced. Therefore, this kind of motor can be made into a large displacement, and can run smoothly at a very low speed, 3. Plunger type high speed hydraulic motor plunger type high speed hydraulic motor is generally axial type
Axial piston motor
In principle, axial piston pump can be used as hydraulic motor except valve type flow distribution. That is to say, axial piston pump and axial piston motor are reversible. The working principle of axial piston motor is that the oil distribution plate and swash plate are fixed, and the motor shaft is connected with the cylinder block to rotate together. When the pressure oil enters the piston hole of the cylinder block through the window of the oil distribution plate, the plunger extends under the action of pressure oil, The swash plate close to the swash plate produces a normal reaction force P on the plunger, which can be divided into axial component force and vertical component force. Q is balanced with the hydraulic pressure on the plunger, and Q causes the plunger to produce a torque on the center of the cylinder block, which drives the motor shaft to rotate counterclockwise. The instantaneous total torque generated by the axial piston motor is pulsating, The change of swashplate angle a, that is, the change of displacement, not only affects the torque of the motor, but also affects its speed and steering. The greater the swashplate angle is, the greater the torque is, and the lower the speed is
Gear hydraulic motor
In order to meet the requirements of forward and reverse rotation, the oil inlet and outlet of gear motor are equal and symmetrical, and there is a separate oil outlet to lead the leakage oil of bearing out of the shell, In order to reduce the torque ripple, the number of teeth of gear hydraulic motor is more than that of pump. The gear hydraulic motor is characterized by poor dry sealing, low capacity efficiency, high input oil pressure and no large torque, Therefore, gear hydraulic motor is only suitable for high speed and small torque. It is generally used in dry construction machinery, agricultural machinery and mechanical equipment with low torque uniformity requirements
High speed hydraulic motor
The motor with rated speed higher than 500r / min belongs to high-speed motor. The basic forms of high-speed motor are gear type, vane type and axial piston type. Their main characteristics are high speed, small moment of inertia, easy to start, brake, speed regulation and reversing
Low speed hydraulic motor
The main characteristics of low-speed hydraulic motor are: large displacement, large volume, low speed, can be directly connected with the working mechanism, without the need for deceleration device, so that the transmission mechanism is greatly simplified. The output torque of low-speed hydraulic motor is large, up to thousands to tens of thousands of nm, Therefore, it is also called low speed high torque hydraulic motor
Calculation of main parameters of hydraulic motor
Main parameters of hydraulic motor
1. Working pressure and rated pressure working pressure: the actual pressure of the input motor oil, which depends on the negative pressure of the motor